Isogeometric Implementation of the High-Order Microplane Model for Softening and Localization

Abstract

In this study, a recently developed higher order microplane (HOM) model for softening and localization, is numerically implemented within a finite element framework based on isogeometric analysis. The HOM model was derived directly from a three dimensional discrete particle model and it was shown to be associated with a high order continuum characterized by independent rotation and displacement fields. Furthermore HOM model was demonstrated to possess two characteristic lengths: the first associated with the spacing of flaws in the material internal structure and related to the gradient character of the continuum; and the second associated with the size of these flaws and related to the micropolar character of the continuum. The displacement-based finite element implementation of this type of continua requires C-continuity both within the elements and at the element boundaries. This motivated the implementation of the concept of isogeometric analysis which ensures a higher degree of smoothness and continuity. NURBS based isogeometric elements were implemented in a 3D setting and with both displacement and rotational degrees of freedom at each control point. The performed numerical analyses demonstrate the effectiveness of the proposed HOM model implementation to ensure optimal convergence in both elastic and softening regime. Particularly, the proposed approach prevents strain localization and spurious mesh sensitivity known to be pathological issues for typical local strain-softening constitutive equations.